3. a. Explain why we can find the area of a 4-cm-by 8 -cm rectangle by multiplying \( 4 \cdot 8 \) by showing how to create equal groups in the situation. b. Discuss how to relate your explanation in p

The sum of the first 31 terms in the new sequence is 5.

Let S = {-4, 0, 2, 3}

New Sequence = {-4, 0, 2, 3, -4, 0, 2, 3, -4, 0, 2, 3, ...............}

The four terms are repeatedly separated, as we can see above. Below are some of the first four terms = -4 + 0 + 2 + 3 = 1

Now, first four terms sum = 1

Next four terms sum = 1.

So sum of first 28 terms is given as

1 + 1 + 1 + 1 + 1 + 1 + 1 = 7

Now we find sum of first 31 terms = 7 - 4 + 0 + 2 = 5

So, sum of first 31 terms of new sequence {-4, 0, 2, 3, -4, 0, 2, 3, -4, 0, 2, 3, ...............} is 5.

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Answer:

L = 20 , B = 10

Step-by-step explanation:

L = 2B

we know perimeter of rectangle = 2( L + B )

By substitution , 2( 2B+ B) =60

4B + 2B = 60

6B = 60

B= 10

L = 2 * B = 2 * 10 = 20

Area of the given trapezoid is 1.8m²

A trapezoid is a polygon having four sides, two of which are parallel and two of which are not. The bases and legs of the trapezoid are known as the parallel and non-parallel sides, respectively. The height or altitude of the trapezoid is defined as the distance between the bases.

The formula, which may be used to determine a trapezoid's area,

[tex]A= \frac{a+b}{2}h[/tex]

where, a and b are the lengths of the two bases and h is the height between two bases.

Given in the trapezoid figure, a= 2, b= 0.9, h is the base upper triangle.

We use the following trigonometric relationship to find the base of the upper triangle,

Apply sine rule in upper triangle with connecting line h.

Sin 45° =  [tex]\frac{h}{1.8}[/tex]

h = 1.8 × Sin 45°

h = 1.8 × 0.707

h = 1.273m

Then, the area of trapezoid:

[tex]A= \frac{a+b}{2}h= \frac{2+0.9}{2}*h[/tex]

[tex]A= \frac{2.9}{2}*1.273[/tex]

A = 1.845m²

Therefore, the area of the trapezoid to the nearest tenth is 1.8m²

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After answering the provided question, we can conclude that As a result, expression the answer is D. 144n.

In mathematics, an expression is a collection of symbols, digits, and companies that portray a statistical correlation or formula. An expression can be a single number, a mutable, or a combination of both of them. Addition, subtraction, proliferation, division, and exponentiation are examples of mathematical operators.  Expressions are used extensively in mathematics, including arithmetic, calculus, and geometry. They are used in mathematical formula representation, equation solution, and mathematical relationship simplification.

According to the scale, 1 inch on the drawing equals 3 feet in real life. As a result, the pool's length is 4 inches x 3 feet/inch = 12 feet. Similarly, the pool's width is 4 inches x 3 feet/inch = 12 feet.

As a result, the pool's area equals the length multiplied by the width, which is:

144 square feet = 12 feet x 12 feet.

As a result, the answer is D. 144n.

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As per the unitary method, Aysha will spend Dh45.45 on souvenirs if she spends Dh100 on games, using the same ratios as on her last trip to the shopping festival.

Now, let's use the unitary method to solve the problem at hand. We know that Aysha wants to spend money using the same ratios as on her last trip to the shopping festival. So, let's find out the ratio of the amount she spent on games to the total amount she spent on all three items (snacks, games, and souvenirs) on her last trip:

Amount spent on games = Dh25

Total amount spent on all three items = Dh20 + Dh25 + Dh10 = Dh55

So, the ratio of the amount spent on games to the total amount spent on all three items is:

Dh25/Dh55

Now, we know that Aysha wants to spend Dh100 on games this time. Let's use the unitary method to find out how much she will spend on souvenirs, given the ratio we just found.

If Dh25 is spent on games, then the total amount spent on all three items will be:

(Dh25/Dh55) * Total amount spent

And we know that the total amount spent is Dh100 (the amount Aysha wants to spend on games). So, substituting this value, we get:

(Dh25/Dh55) x Dh100

Simplifying this expression, we get:

Dh45.45

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Addressing issue hand, we state that Therefore, the linear equation solution to the system of equations is: x = 0.5, y = 0.1667, z = -0.5 and x = 0.500, y = 0.167, z = -0.500

In algebra, a linear equation refers to one with its form y=mx+b. B is the gradient, and m is the esta. The preceding clause is commonly referred to as a "linear function with two variables" so even though y and x are variables. Bivariate linear equations are linear equations with two variables. There are several linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. When an equation seems to have the structure y=mx+b, where m is the slope and b is the y-intercept, it is said to be linear. When a measurement seems to have the formula y=mx+b, both with m identifying its slope and b denoting the y-intercept, it is said to be linear.

values of x, y, and z, we can use the system of equations

3x - 2y + z = 1

2x + y - z = 0

x + 2y + 3z = -1

We can use Gaussian elimination or any other suitable method to solve the system. Here's one way to do it:

3x - 2y + z = 1          (eq. 1)

2x + y - z = 0           (eq. 2)

x + 2y + 3z = -1         (eq. 3)

       3x - 2y + z = 1          (eq. 1)

       0.6667x + 1.3333y - 1.3333z = -0.6667    (eq. 2')

       -0.3333y + 2.3333z = -1.3333    (eq. 3')

       3.3333x - 0.3333z = 0.1667    (eq. 1')

       0.6667x + 1.3333y - 1.3333z = -0.6667    (eq. 2')

       2.1667z = -1.0833    (eq. 3')

       z = -0.5

       y = 0.1667

       x = 0.5

Therefore, the solution to the system of equations is:

x = 0.5, y = 0.1667, z = -0.5

x = 0.500, y = 0.167, z = -0.500

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The brick weighs 3.4 kilograms.

Quantities are values that can be measured or counted. They are typically represented by numerical values and units of measurement.

Let's assume that the weight of each brick is the same. Let's also denote the weight of each brick by "w" (in kilograms).

On one side of the scale, we have 9 bricks and 5 kilograms. So the total weight on this side is:

Total weight = (9 x w) + 5

On the other side of the scale, we have 4 bricks and 22 kilograms. So the total weight on this side is:

Total weight = (4 x w) + 22

Since the bricks on the scale are in balance, the total weight on both sides must be equal. Therefore, we can set the two expressions for total weight equal to each other and solve for w:

(9 x w) + 5 = (4 x w) + 22

Expanding and simplifying the equation, we get:

5 x w = 17

Therefore, the weight of each brick is:

w = 17 / 5

w = 3.4 kilograms

So each brick weighs 3.4 kilograms.

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Glenn has 1/20 of the granola bar left.

How to find?

If Glenn has 2/5 of a granola bar and eats 7/8 of it, we need to find out how much is left.

First, we need to find out how much Glenn ate. To do this, we can multiply the fraction of the granola bar that Glenn had (2/5) by the fraction that he ate (7/8):

2/5 × 7/8 = (27)/(58) = 14/40

Simplifying this fraction, we get:

14/40 = 7/20

So, Glenn ate 7/20 of the granola bar.

To find out how much is left, we can subtract the fraction that he ate from the fraction that he had:

2/5 - 7/20

To subtract these fractions, we need to find a common denominator. The least common multiple of 5 and 20 is 20, so we can convert both fractions to have a denominator of 20:

2/5 = 8/20

7/20 = 7/20

Now we can subtract the fractions:

8/20 - 7/20 = 1/20

So, Glenn has 1/20 of the granola bar left.

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In a case whereby concrete sidewalk is being put around a square park. If the diagonal line across the center of a square park is 24 feet, the exact length of each side is 12 feet.

Based on the given condition from the question, We know that A diagonal is a line segment that joins two opposing polygonal vertices (or corners). In other terms, a diagonal is a line segment that joins two polygonal vertices that are not next to one another. One type of straight line is the diagonal. There is no straight up, down, or across in a diagonal line. It is a line that joins two shape's corners.

Then we can formulate as 24/2

= 12 feet.

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Answer:

600ft²

Step-by-step explanation:

Volume of a cube V = a³

a³ = 1000

Cube root of both sides

a = 10ft

Surface area A =6a²

A = 6 x 10 x10 ft²

Answer:

600 feet²

Step-by-step explanation:

1) Break down the info

To answer this question we have to figure out the values of the sides. As it is a cube all sides should have the same area and length!

We know that the equation for volume is...

This means that to simply find the sides, we can cube root 1000

Let's check...

2) Find the surface area

We now know that the sides are 10 feet each so to find the surface area is [tex]6a^2[/tex] where a is the length of one side!

We can solve the question by plugging our numbers into the equation...

Our surface area is 600 feet!

Hope this helps, have a lovely day! :)

To find the product of the face values (the values of the digits as they appear in the number) of all digits in 91250, we can simply multiply the face values of each digit together.

The face value of a digit is simply the value of the digit itself, regardless of its position in the number.

So, we have:

9 * 1 * 2 * 5 * 0 = 0

Note that the face value of the digit 0 is 0, so any product that includes a 0 will also be 0.

Therefore, the product of the face values of all digits in 91250 is 0.

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Answer:

1st=3/50

2nd=2/50

3rd=1/50

thats is if the only possible number you can roll are only from 2,6 not 1,6

To calculate the proportion of Dave's wages spent on rent, divide the amount of rent by his monthly earnings and multiply by 100 to obtain the percentage Rent as a percentage of earnings = (Rent / Earnings) x 100%.

When we substitute the provided values, we get: Rent as a percentage of wages = (840 / 2300) x 100% = 36.5% As a result, to the closest hundredth of a percent, Dave spends about 36.5% of his salary on rent. This indicates that rent accounts for around 36.5% of Dave's monthly income. This proportion might provide us with information about Dave's financial status. Financial experts often advise consumers to spend no more than 30% of their income on housing expenditures, including rent and utilities. In Dave's situation, his rent is somewhat higher than the recommended amount. This might signal that he is struggling to make ends meet or that he should look into more cheap housing possibilities. If David can easily pay his existing rent, this percentage may not be a reason for concern.

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Answer:

Step-by-step explanation:

-14.76: Rational

-sqrt(64): 64 is a perfect square so it is rational

1.4444444… rational numbers repeat their decimal digits at one point or another, so this is rational

pi is irrational, so 19pi is irrational.

sqrt(2)*sqrt(2) is rational, but not 2sqrt(2). Irrational.

The airplane is approximately 1.7 miles from the runway at the start of the approach.

What is trigonometry?

Trigonometry, the branch of mathematics concerned with specific functions of angles and their application to calculations. There are six functions of an angle commonly used in trigonometry

To solve this problem, we need to use trigonometry. The angle of descent is 7 degrees, which means that the angle between the horizontal ground and the plane's flight path is 7 degrees. We can use the tangent function to find the distance from the runway:

tangent (7 degrees) = opposite / adjacent

The opposite side is the height of the plane above the ground, which is 1069 feet. The adjacent side is the distance from the plane to the runway, which we need to find.

tangent (7 degrees) = 1069 / adjacent

We can solve for the adjacent side by multiplying both sides by the denominator:

adjacent = 1069 / tangent(7 degrees)

Using a calculator, we get:

adjacent = 1069 / 0.122173048

adjacent = 8743.3 feet

To convert this to miles, we divide by the number of feet in a mile:

adjacent = 8743.3 / 5280

adjacent = 1.655 miles

Rounding to the nearest tenth of a mile, we get:

The airplane is approximately 1.7 miles from the runway at the start of the approach.

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We can use the rule for h(x) to calculate the output values of the function for each given input value of x, which allows us to complete the function table mathematically.

In mathematics, a function is a rule or mapping that assigns a unique output value for every input value in a specified set

To complete the function table mathematically, we need to use the given rule for the function h(x) = 5x - 1 and substitute the given values of x to find the corresponding values of h(x).

For example, when x = -5, we can find the corresponding value of h(x) as follows:

h(-5) = 5(-5) - 1

= -26

Similarly, we can substitute x = -4, 1, 2, and 3 into the rule for h(x) to find the corresponding values of h(x) for each input value of x. This gives us the completed function table:

x        h(x)

-5      -26

-4      -21

1        4

2       9

3       14

Therefore, we can use the rule for h(x) to calculate the output values of the function for each given input value of x, which allows us to complete the function table mathematically.

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Answer:

5'6 and 5'0

Step-by-step explanation:

Put the graph in order of dots

4'11- 1

5'1- 1

5'3- 1

5'6- 1

5'0- 2

5'2- 2

5'5- 2

5'4- 5

The middle values are 5'6 and 5'0, so that should be the answer.

The units for base area calculations are squared units and the units for volume calculations are cubed units. This is because the area and volume calculations require different equations and different units of measurement.

The units on your base area calculations should be squared units, such as square meters, square centimeters, square inches, or square feet. This is because the area of a two dimensional shape is the amount of space occupied by the shape and is calculated by taking the length of the base and multiplying it by the width of the base. For example, if a rectangle has a length of 5 meters and a width of 3 meters, the area of the rectangle would be 5 x 3 = 15 square meters.

The units on your volume calculations should be cubed units, such as cubic meters, cubic centimeters, cubic inches, or cubic feet. This is because the volume of a three dimensional shape is the amount of space occupied by the shape and is calculated by taking the area of the base and multiplying it by the height of the shape. For example, if a cube has an area of 15 square meters and a height of 4 meters, the volume of the cube would be 15 x 4 = 60 cubic meters.

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Answer:

The volume of one cone-shaped cup can be calculated using the formula V = (1/3)πr^2h, where r is the radius of the cone and h is the height. Substituting the given values, we get:

V = (1/3)π(5 cm)^2(10 cm)

V ≈ 261.8 cm^3

Therefore, one cup can hold approximately 261.8 cubic centimeters of flower petals.

To find the total volume of petals that all 150 cups will hold, we can multiply the volume of one cup by the total number of cups:

Total volume = 150 cups × 261.8 cm^3/cup

Total volume ≈ 39,270 cm^3

Rounding to the nearest whole number, we get that the total volume of petals that all the cones will hold is approximately 39,270 cubic centimeters.

Answer:

I forgot how to do this sorry

The National League variance is 0.00020 and the standard deviation is 0.0141 while the American League variance is 0.000191 and the standard deviation is 0.0138.

According to question, the team batting averages for Major League Baseball in a certain year are represented below. We have to find the variance and standard deviation for each league. Given below is the table of team batting averages in National League and American League.

National League   American League
 .240                .237
 .242                .244
 .240                .251
 .247                .233
 .256                .243
 .249                .248
 .256                .238
 .240                .241
 .243                .250
 .237                .238

We know that,

variance = (1/N)* Σ(xi - µ)²
Standard deviation = √variance

National League:
The mean of National League, µ = (0.240 + 0.242 + 0.240 + 0.247 + 0.256 + 0.249 + 0.256 + 0.240 + 0.243 + 0.237)/10 = 2.443/10 = 0.2443.
Substitute the values in the formula, variance = (1/10)* Σ(xi - µ)² = (1/10)* [ (0.240 - 0.2443)² + (0.242 - 0.2443)² + (0.240 - 0.2443)² + (0.247 - 0.2443)² + (0.256 - 0.2443)² + (0.249 - 0.2443)² + (0.256 - 0.2443)² + (0.240 - 0.2443)² + (0.243 - 0.2443)² + (0.237 - 0.2443)² ]= 0.00019749
Standard deviation = √variance = √0.00019749 = 0.01405
The National League variance is 0.00020 and the standard deviation is 0.0141

American League:
The mean of American League, µ = (0.237 + 0.244 + 0.251 + 0.233 + 0.243 + 0.248 + 0.238 + 0.241 + 0.250 + 0.238)/10 = 2.423/10 = 0.2423
Substitute the values in the formula, variance = (1/10)* Σ(xi - µ)² = (1/10)* [ (0.237 - 0.2423)² + (0.244 - 0.2423)² + (0.251 - 0.2423)² + (0.233 - 0.2423)² + (0.243 - 0.2423)² + (0.248 - 0.2423)² + (0.238 - 0.2423)² + (0.241 - 0.2423)² + (0.250 - 0.2423)² + (0.238 - 0.2423)² ]= 0.00019119
Standard deviation = √variance = √0.00019119 = 0.01383

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Answer:

6.8 I think

Step-by-step explanation:

5. Vertex: (2, 2)

Dοmain: All real numbers

Axis οf symmetry: x = 2

Increasing οn: (-∞, 2)

Decreasing οn: (2, ∞)

A quadratic functiοn is a pοlynοmial functiοn οf degree 2, where the highest pοwer οf the variable is 2. It has a parabοlic graph and is cοmmοnly used tο mοdel real-wοrld phenοmena.

5. Vertex: (2, 2)

Dοmain: All real numbers

Axis οf symmetry: x = 2

Increasing οn: (-∞, 2)

Decreasing οn: (2, ∞)

7. Vertex: (2, 3)

Dοmain: All real numbers

Axis οf symmetry: x = 2

Increasing οn: (-∞, 2)

Decreasing οn: (2, ∞)

Range: y ≥ 3

6.Vertex: (-2, -4)

Vertical shift: -4 units

Hοrizοntal shift: -2 units

Width: Cοmpressed hοrizοntally by a factοr οf 1/3

Reflected: Nο

8. Vertex: (-2, -2)

Vertical shift: -2 units

Hοrizοntal shift: -2 units

Width: Stretched by a factοr οf 3 in the vertical

Reflected: Nο

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The 95% confidence interval for tthe population mean, μ of all venture-capital investments in the fiber optics business sector is equals to the 4.472 ≤ μ ≤ 7.990 that is ( 4.472, 7.990).

We have a random sample of venture capital investments in the fiber optics business sector.

Sample size, n = 10

Standard deviations, σ = $2.84 million

Sum of data, ∑xᵢ = $62.32 million

Confidence interval, CI = 95% = 0.95

We have to determine the 95% confidence interval for the mean amount.

Sample mean is defined as the sum of observations divided by number of observations. Mathematically, X-bar

= ∑xᵢ /n

= 62.32/10 = 6.232

Now, using the Z distribution table, the critical value at 0.05 significance level for two tailed test is = Z₀.₀₅/₂ = Z₀.₀₂₅

= 1.96

So, 95% confidence interval for the population mean is written as

CI₀.₉₅ = X-bar - Z(σ/√n ) ≤ μ ≤ X-bar + Z(σ/√n)

= 6.232 - 1.96(2.84/√10) ≤ μ ≤ 6.232 +

1.96(2.84/√10)

= 6.232 - 1.760 ≤ μ ≤ 6.232 + 1.760

= 4.472 ≤ μ ≤ 7.990

Hence, required interval is ( 4.472, 7.990).

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Answer:

[tex]y=(x+4)^2-8[/tex]

Step-by-step explanation:

[tex]y=x^2-8x-8[/tex]

complete the square.

[tex](x+4)^2-8[/tex]

set y equal to the new right side.

[tex]y=(x+4)^2-8[/tex]

Hope this helps!

Brainliest is much appreciated!

Answer:

Step-by-step explanation:

a = 1

c = -8

b= -8

the formula of vertex form is a(x-h)^2 +k = y

First find H and k using the formula -b/2a = h

h = 4

so, k = -24

y =1(x-4)^2 -24

The game is fair in the sense that the expected value is not negative.

The expected value serves as a gauge for a random variable's typical value. It is determined by multiplying each of the variables' potential outcomes by its corresponding probability, then adding the resulting products. In order to comprehend the typical outcome of a random process and determine if a given course of action is likely to be lucrative or not, the expected value is a valuable tool in decision-making.

The probability of getting a spade is 13/52 or 1/4.

The probability of getting anything else is 3/4.

he expected value of playing the game can be calculated as:

Expected value = (probability of winning x amount won) - (probability of losing x amount lost)

Expected value = (1/4 x $10) - (3/4 x $3)

Expected value = $2.50 - $2.25

Expected value = $0.25

Since the expected value is positive, this means that on average, you can expect to win $0.25 for every time you play the game.

Hence, game is fair in the sense that the expected value is not negative.

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The only common factor is [tex]b^{2}[/tex] so the GCF is [tex]14b^{3}[/tex] and [tex]5b^{2}[/tex] is [tex]b^{2}[/tex]

The term "common" means "same for both." The two numbers' common factor is one that applies to both numbers.

The common factor between [tex]6[/tex] and [tex]10[/tex] is [tex]2[/tex], for instance. Although it is not the sole quality shared by each number, it is a trait that they both have in common.

To find the GCF of [tex]14b^{3}[/tex] and [tex]5b^{2}[/tex] we need to find the largest factor for both

[tex]14b^{3}[/tex] = 2*7*[tex]b^{2}[/tex]*[tex]b[/tex]

[tex]5b^{2}[/tex] = [tex]5*b^{2}[/tex]

Therefore the only common factor is [tex]b^{2}[/tex] so the GCF is [tex]14b^{3}[/tex] and [tex]5b^{2}[/tex] is [tex]b^{2}[/tex]

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The combination of weights listed above would balance a mass of 45 grams on the balance scale.

A instrument used to determine an object's mass is a balancing scale. It is made out of a beam suspended from a fixed point, with two pans or trays hanging from either end. The beam is balanced when the mass of the objects on one tray equals the mass of the objects on the other tray. The principle of moments, according to which, when the beam is in equilibrium, the moment of force on one side of the balance is equal to the moment of force on the other, governs how a balancing scale functions.

Given that, Rosa can balance a mass of 45 grams using the given combinations.

Thus, total weight on the two sides are:

Left side: 32g + 6g + 6g + 1g = 45g

Right side: 8g + 8g + 2g + 2g = 20g

Hence, the combination of weights listed above would balance a mass of 45 grams on the balance scale.

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Answer:

-10

Step-by-step explanation:

BODMAS

Brackets

Of

Division

Multiplication

Addition

Subtraction

●When simplifying an equation follow the above order.

•Since division comes before subtraction, first divide -24 by -8 to get 3

•Then subtract 13 from 3 to give you -10.

Answer:0.833333

Step-by-step explanation:

Answer:

0.08333

Step-by-step explanation:

pls mrk me brainliest

Answer:

its a negative slope because the battery is going down, not staying the same, or going up

Step-by-step explanation: